Generally, triaxial accelerometers produce output signals related to acceleration sensed in three linearly independent directions. More specifically, the triaxial accelerometer may include stress sensor elements intended to align with each of the three Cartesian coordinate axes. Thus, relative to each other, each stress sensor element may be configured to align in the x-axis, in the y-axis, and in the z-axis, respectively. The stress sensor elements may include force sensitive resonators, strain gauges, or the like, to allow measuring an output related to a change in position, a change in the load, or the like, of the inertial proof mass or other structure. The axial related output in an accelerometer (in three directions) may be referred to as a triad or a measurement triad.
Some triaxial accelerometers may include two or more sensor elements in one or more axial direction (i.e., two sensor elements in one or more of the three axes). Thus, a triaxial accelerometer having, for example, two sensor elements in each orthogonal direction includes two measurement triads. Alternatively, for a device having asymmetric construction, (i.e., having unequal numbers of sensor elements in each direction) additional measurement triads may be defined mathematically by including the output of some of the sensor elements in more than one measurement triad. Thus, a triaxial accelerometer having, for example, two sensor elements in only one direction and single sensor elements in each of the remaining directions, two complete measurement triads may be defined by including the single sensor elements in the definitions of both measurement triads.
However, the measurement triad output is often calibrated to minimize error between the output recorded and the actual acceleration applied to the accelerometer. The errors may be the result of variances in the construction of the sensor elements, such as strain gauge variances or variances in the composition or output of individual force sensitive resonators. Errors may also result from an inexact orientation of each sensor element in relation to the others and to the axes along which they are intended to be oriented. Accordingly, calibration operations may include identifying a correction term or terms (e.g., calibration constants or correction constants) to apply to the measurement triads, so as to generate meaningful output that can be used to make determinations and measurements relational to, for example, a gravity field or other known vector.
Traditionally, for accelerometers having more than one measurement triad, calibration optimizations are performed individually for each triad, and then the outputs of the individually-calibrated triads are averaged to produce the output of the accelerometer. However, averaging these individually-calibrated outputs may not produce the most accurate results. Additionally, to correct for misalignment or inexact alignment of the individual sensor elements, these traditional methods do not simultaneously optimize, in one step, the outputs for situations in which the sensor elements of a triad may not necessarily be orthogonal with respect to other sensor elements of the triad, and/or the independent Cartesian coordinate system suggested by each individually-calibrated triad may not align with one another. Thus, performing individual alignment calibrations and rotation transformation in separate steps may yield inaccuracies.
Thus, there exists a need to for systems and methods for calibrating triaxial accelerometers.